Comment on ``Duality relations for Potts correlation functions''

TL;DR

This paper critically examines Wu's method for relating Potts model correlations to dual partition functions, demonstrating its limitations for higher-order correlations due to complex connectivity issues.

Contribution

It clarifies the limitations of Wu's approach by explicitly analyzing four-point correlations, showing the method's inapplicability to more complex cases.

Findings

Wu's method applies only to three-point correlations

Higher correlations involve non-nested connectivities

The method does not extend straightforwardly to four-point correlations

Abstract

In a recent paper by Wu (Phys. Lett. A 228, 43-47 (1997)) the three-point correlation of the q-state Potts model on a planar graph was related to ratios of dual partition functions under fixed boundary conditions. It was claimed that the method employed could straightforwardly be applied to higher correlations as well; this is however not true. By explicitly considering the four-point correlation we demonstrate how the appearence of non-well-nested connectivities invalidates the method.